A logistic model for precise tomato fruit-growth prediction based on diameter-time evolution

Abstract

Monitoring tomato fruit growth in large greenhouse environments is crucial for estimating harvest volume and maximising labour efficiency. Mathematical modelling is commonly used to characterise crop and fruit growth and to understand crop responses to environmental influences. This study presents a logistic approach for estimating tomato fruit maturity based on fruit diameter. A set of logistic models were evaluated, and their precision and ability to forecast tomato fruit growth were analysed. Non-linear least square regression was used to fit each model to individual tomato fruits from a sample of over 600 fruits of two species (small and large fruit-bearing tomatoes) grown within one year. The focus was on fruit diameter and the necessary measurement precision for fruit maturity estimation. Low-dispersion variables were identified within our logistic model functions, and fruit species-specific model parameters were determined. Furthermore, we reduced the number of regression variables by identifying parameters of low variance. This allowed for high prediction precision ( > 80%) at the early fruit maturity stages ( < 30%). The fruit diameter data were collected manually using a caliper. Our results establish an upper limit for the measurement precision of automated fruit size estimation approaches utilising photogrammetry, with an optical range of 98% for 3 mm and 90% for 5 mm precision. • Long and short term Tomato fruit size prediction. • High precision fruit yield forecasting. • Optimised tomato fruit growth modelling and comparison between models. • Upper limit estimation for growth predictability.

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